Arithmetic Sequence/Series?
Jamila is making a triangular wall with building blocks. The top row has one block, the second row has three, the third row has five, and so on. How many rows can she make with a set of 100 blocks?
How do i solve this using Arithmetic series/sequences equations?
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Its sum of series of odd numbers.
First row : 1
second row: 3
third row : 5 and so on.
So its 1+3+5+7+9. ........ (2n-1) = 100
(2n -1 ) is any Nth term of the series.
Now sum of series of odd numbers is n^2.
Therefore, n^2= 100
so n= 10.
Total number of rows =10.
1+3+5+...... < 100
((1+2n-1)/2)*n = n^2
n^2 = 100
n= 10
10 rows.
a4 = 5 = 4d + c Sum of first 6 words = 3(a1 + a6) = 10 => a1 + a6 = 10/3 = d + c + 6d + c = 7d + 2c -8d + 7d = -10 + 10/3 => -d = -20/3 => d = 20/3 c = 5 - 80/3 = -sixty 5/3 Sum of first 19 words = 19/2 * (-15 + one 0 five) = 855